Advanced Probability Theory

Wednesday 11:15-12:50, Seminarraum 9 (OMP 1)
Thursday 11:15-12:50, Seminarraum 8 (OMP 1)

Summary: The lecture presents the most important results and concepts of the modern probability theory, using the measure-theoretic framework, in the context of infinite sequences of random variables, i.e. stochastic processes in discrete time. It gives an introduction to basic convergence results for such sequences: laws of large numbers, central limit theorem, large deviation for independent sequences; convergence of stochastic series; martingale convergence theorems; convergence of Markov chains. We discuss weak convergence of probability measures on function spaces and construct the Brownian motion by means of Donsker's theorem.


Lecture notes:

Exam questions: [PDF]

Proseminar to Advanced Probability Theory

Thursday 13:15-14:00, Seminarraum 8 (OMP1)

Instructor:Tobias Wassmer

Summary: The proseminar complements the lecture with examples, exercises and short talks.

Problems for solution: TBD